A236399 Left factorial !p, where p = prime(n).

2, 4, 34, 874, 4037914, 522956314, 22324392524314, 6780385526348314, 1177652997443428940314, 316196664211373618851684940314, 274410818470142134209703780940314, 382630662501032184766604355445682020940314, 836850334330315506193242641144055892504420940314

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..87

Romeo Mestrovic, Variations of Kurepa's left factorial hypothesis, arXiv:1312.7037 [math.NT], 2013.

Formula

a(n) = Sum_{k=0..(prime(n)-1} k!. - G. C. Greubel, Mar 29 2019

Maple

lf:=n->add(k!, k=0..n-1);
[seq(lf(ithprime(n)), n=1..30)];
# 2nd program:
A236399 := proc(n)
    A003422(ithprime(n)) ;
end proc:
seq(A236399(n), n=1..5) ; # R. J. Mathar, Dec 19 2016

Mathematica

leftFac[n_] := Sum[k!, {k, 0, n - 1}];
a[n_] := leftFac[Prime[n]];
Array[a, 13] (* Jean-François Alcover, Nov 24 2017 *)

Prog

(PARI) vector(15, n, sum(k=0, prime(n)-1, k!)) \\ G. C. Greubel, Mar 29 2019
(Magma) [(&+[Factorial(k): k in [0..(NthPrime(n)-1)]]): n in [1..15]]; // G. C. Greubel, Mar 29 2019
(Sage) [sum(factorial(k) for k in (0..(nth_prime(n)-1))) for n in (1..15)] # G. C. Greubel, Mar 29 2019

Crossrefs

A subsequence of A003422.

Sequence in context: A306582 A103625 A006989 * A132529 A027681 A348094

Adjacent sequences: A236396 A236397 A236398 * A236400 A236401 A236402

Keyword

nonn

Author

N. J. A. Sloane, Jan 29 2014

Status

approved